The Al Ain striker was absent for Ghana's opening Group D defeat to Senegal after suffering with malaria.
However, he played the entirety of Friday's contest in Mongomo and kept his composure with a cool finish in stoppage time to settle a tight contest 1-0.
Head coach Grant subsequently praised the former Sunderland man's contribution on and off the pitch.
"Asamoah is a great player, and he has a fantastic attitude," he said.
"He was sick, but he played 90 minutes and scored in the end.
"He's a great player, but also a great personality. It's not only the victory of a player, but a whole team."
Winger Andre Ayew believes a tactical switch from Grant at half-time paved the way for Ghana's victory.
"We just wanted to win this game, we won it the hard way in the last minute," he said.
"The coach changed tactics to play more offensively, because we had to win. I am not surprised we won, we had the quality to win."
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